Evidence that fold-change, and not absolute level, of β-catenin dictates Wnt signaling

In the canonical Wnt pathway, binding of the Wnt ligand to its transmembrane receptors leads to an inhibition of the degradation of β-catenin; as a result, β-catenin accumulates to a point where it activates target genes. Using mathematical modeling and experiments in mammalian cells, we examined the robustness of the β-catenin response to Wnt stimulation. We found that the final (post-Wnt) level of β-catenin is very sensitive to all perturbations in the Wnt signaling pathway, such that mild genetic or environmental variation would be expected to change the final level of βcatenin, and alter the output of the pathway. By contrast, one unusual parameter was robust: the fold-change in β-catenin (postWnt level / pre-Wnt level). Furthermore, in Xenopus embryos, dorsal-anterior development and the corresponding target gene expression are robust to the same perturbations that alter the final level but leave the fold-change intact. These results suggest: First, despite noise and variation, within a range the cell maintains a constant fold-change in β-catenin for a given Wnt stimulation. Second, the transcriptional machinery downstream of the Wnt pathway is constructed to read the robust fold-change and not simply the final level of β-catenin. In analogy to Weber’s law in sensory physiology, some gene transcription networks may be tuned to respond to fold-changes, rather than absolute levels of signals, as a way to reduce the consequences of stochastic, genetic and environmental variation.